Ignore all other reviews for this class, as most of them are either outdated or from math people who love sitting at their desks for 10+ hours a week thinking about theory. This class, if not already known, is the advanced mathematical offering of CS 181, meaning that instead of studying application, you study the theory of this class. The lectures are "lead" by students, which often involve questions not pertaining to curriculum and you often go off on tangents. Additionally, this class format creates an environment where you do not know what you need to learn and what is irrelevant, often making the class even harder than before. Also, don't get me started on the homework, which by his syllabus, takes 15-20 hours each.
Summary: Avoid this class with Sahai at all costs unless you like torturing yourself with math theory.

Prof. Sahai is a very good lecturer and has made CS 181 a breeze for us. He does challenge his students but he makes sure everyone can succeed if they want to.

I took this class in Winter 2012. This class is extremely challenging. However, I would say I learned the most in this class out of any other class.

The review about lectures sucking is completely wrong. I guess whoever wrote that review only went to lecture once when we had a bad day. Sahai encourages questions in lecture by offering extra credit points for participating (1/4 percent per attempted answer) and very often the class as a whole will help solve the problem or derive the theorem's proof that Sahai is focusing on that day.

The homeworks take about 10-16 hours a week. Start early! Sahai and the TA (Abishek) often repeat this and say that the only way to solve these problems is to read the book, go to lecture, collaborate with your classmates (but not plagiarize), and repeatedly bang your head against the problems until you have an epiphany. It's tough, but they're right. Once you solve a problem, you gain a pretty profound understanding of the material, and that's a really satisfying feeling.

With that said, some of the homework problems are indeed rigorous proofs. Sahai warned us that the winter offering of CS 181 is a more challenging offering, and that we are expected to have knowledge of proofs. If we don't, he gives a link/guide on how to write proofs and different methods, such as proof by contradiction (the most common one in this class; just about every proof is with this method), unwinding the definition, proof by induction (also a common method), applying the Pigeonhole Principle, and so on. In addition, all proofs that Sahai does in the class and that Abi does in discussion are rigorous proofs, so you can learn by their examples.

Discussion was an extension of lecture where new material was taught in addition to clarifying old topics. Abi also went over the homework a little bit but rarely gave hints.

The midterm was easier than the homework, because we only got 2 hours to do it in class. The final was very challenging, but not unreasonable, and it was take-home format so we were given a week to do it. There is no collaboration allowed on the final.

Office hours were very effective. No hints as to the kind of test problems to expect were given during OH.

His curves are not that generous. I would say that he only gives about ~15% A's; even though everything busts their butt, most people will get B's. If you are looking for a cakewalk class, don't take Sahai. If you are looking to learn a lot, and maybe get a B even if you worked really hard, then take this class!

Absolutely fantastic professor. Every lecture was well prepared, organized, and interesting. Class was difficult but so interesting that students were encouraged to work their hardest. I would love to have this teacher for more classes.